Can Standard Deviation Be Negative? No (See Why)

In one word: No.

Why Standard Deviation Can’t Be Negative

First, let’s stop for a moment and think about what standard deviation represents.

It measures variability in a data set.

When you have some set of numbers and calculate its standard deviation, the resulting number tells you to what extent the individual numbers in the set are different from each other. If all are about the same (like 252, 249, 253, 251, 254), standard deviation will be relatively small. If there are big differences (like 252, 11, 840, 305, 64, 5846), standard deviation will be much bigger.

What if all the numbers in the data set are exactly the same (like 252, 252, 252, 252, 252, 252)? Then standard deviation will be exactly zero.

Can you get an even smaller standard deviation (which would have to be negative)? No. You can’t have a data set which is less diverse than one where all numbers are the same, right?

To conclude, the smallest possible value standard deviation can reach is zero. As soon as you have at least two numbers in the data set which are not exactly equal to one another, standard deviation has to be greater than zero – positive. Under no circumstances can standard deviation be negative.

Why Standard Deviation Can’t Be Negative Mathematically

The above was the common sense explanation. There is also a mathematical explanation, based on the way standard deviation is calculated.

Standard deviation is the square root of variance, which is the average squared deviation from the mean and as such (average of some squared numbers) it can’t be negative. See more detailed explanation here: Can variance be negative?


Related pages


standard deviation of returns calculatorcoefficient in excelmacd definitioncontinuously compounded returnblack-scholes-merton option pricing modelmoving standard deviation excels&p 500 vixpayoff chartpowershares etnoption spread calculatormean sd calculatoretf short sp500cumulative probability exceloption straddle calculatormedian function in excelpositive kurtosismacd trading strategywhat is delta hedginghow to calculate the median in exceloption theta formulamsft financevix cashexcel formula to calculate average percentageshortcut formula for variancevix chart yahoospy spxdefinition skewnesscalculating volatility of a stockoption straddle strategiesexponential function in excel 2010positive and negative number calculatorimplied volatility wikiarithmetic mean for grouped data examplestandard deviation stock calculatorvariance calculation excelprofit loss formula in excelberkshire hathaway 13frsi stock marketfinance standard deviation calculatorcost variance calculatornormdist excel functioninventory purchases formulafinding the median in excelvolatility etf 3xvar value at risk formulahow is vix calculatedmacro hedge fund strategyblack scholes merton calculatorapple stock history calculatordelta hedging formulafree black scholes calculatornegatives and positives calculatordirectional strategy hedge fundsoption delta hedgevxx tickervariance finance formuladivergence macddelta hedging options examplevix inverse etfvix futures term structurehow to calculate the median in excelmsft stock split historyusing macd to tradewacc meaningfixed income arbitrage examplehow to write ln in excelipath etntvix prospectusstandard deviation calculator in excelpayoff of call optionstandard deviation and variance calculatorsample variance excel formulaannualize returnsunbiased variance formulakurtosis examplesvariance shortcut formulablack scholes model calculator